In the field of radio communication in telecommunication networks, interference alignment (IA) is a recently developed precoder technology, which provides significant gains in interference channels compared to conventional orthogonal medium-sharing methods. A few known precoder technologies are discussed in “Interference alignment and degrees of freedom of the K user interference channel”, to V. Cadambe and S. A. Jafar, published in IEEE Transactions on Information Theory, vol. 54, No. 8, p. 3425-3441 in August, 2008. However, implementation of interference alignment methods in existing systems faces a lot of challenges. The necessity of channel knowledge at the transmitters is one of the major issues. This is not practical to achieve in many situations. Moreover, the accuracy of channel state information (CSI) provided to the transmitters should increase as the power increases in order to guarantee the Degrees of Freedom (DoF) gains promised by interference alignment. Therefore, transmission systems which acquire the CSI through feedback from a signal receiving node, such as Frequency Division Duplex (FDD) systems, become less favourable for implementation of interference alignment since potential gains of interference alignment appear at high powers.
For Time Division Duplex (TDD) systems, every base station (BS) can estimate its downlink channels from the uplink transmission phase due to the assumed reciprocity of the channels, i.e. the interference is assumed to be similar in uplink and downlink. However, since interference alignment requires global CSI, which will be explained in section “IA precoding schemes” below, the base stations need to quantize the measured CSI and to share it with other base stations. The CSI may be shared with a central unit in charge of interference management. The measured CSI is usually sent on backhaul links. These backhaul links have limited capacity and hence should be exploited efficiently when sharing the CSI. Since there is typically a significant amount of CSI to share, a code-book based system is used to quantize the CSI into a code-book based CSI to reduce the amount of bits to send. With the code-book based CSI, each BS has knowledge of the code-book a priori and the complete CSI information is represented and conveyed in terms of a code-book index. The efficiency of the code-book system typically depends on how the code-book based CSI has been quantized.
IA Preceding Schemes
In the literature, several IA precoding schemes have been proposed that exploit one or several of the orthogonal dimensions time/frequency/space.
FIG. 1 illustrates downlink, or uplink, spatial IA for MIMO interference channel with K=3 transmitter-receiver pairs. The base stations, shown as Tx, are connected via backhaul links to a IA central unit, where three corresponding IA precoders V1, V2, V3 are calculated. Each node, i.e. transmitter and receiver, is equipped with M number of transmit antennas and N number of receive antennas. Let Hnm denote the channel from transmitter m to receiver n. Moreover, for the symmetric setup where M=N, each transmitter can send at most M/2 spatial information streams and simultaneously align the interference at the receivers within the remaining M/2 dimensions. As shown in “Interference alignment and degrees of freedom of the K user interference channel”, mentioned above, a first IA precoder V1 can for this particular case be found as the solution to the following eigenvalue problem:V1=(H31)−1H32(H12)−1H13(H23)−1H21V1.  (Eq. 1)where the remaining two precoders V2, V3 are obtained from the relationsV2=(H32)−1H31V1 and V3=(H23)−1H21V1.  (Eq. 2)
It can be seen from (Eq. 1) and (Eq. 2) that only the cross channels, Hnm, m≠n, are required at the IA central unit, which is responsible for the IA precoder calculation. How to practically obtain this channel information in an efficient way is a non-trivial system design issue which is discussed briefly in the following.
We distinguish between interference alignment (IA) for the downlink, where the IA precoders are employed at the base stations, or the transmitters (Tx), and IA for the uplink, where the precoders are employed at the mobile stations (MSs), or the receivers (Rx).
Firstly, considering IA for the downlink, the mobile stations first transmit orthogonal pilots to allow the base stations to measure all uplink (UL) direct- and cross-channels between the mobile stations and the base stations, i.e. Hnm. By assuming channel reciprocity, which essentially limits the scheme to time division duplex (TDD), the measured uplink channels provide estimates for the corresponding downlink channels. These estimates are sent to the IA central unit that calculates the precoders e.g. via (Eq. 1) and (Eq. 2). The obtained precoders are then sent to their respective base stations and subsequently used at a pre-determined time instant with known DL pilots to allow the kth MS to estimate the effective channel, HkkVk, and an appropriate receiver filter as shown in the above mentioned “Interference alignment with non-ideal CSI”. Note that the described scheme does not require any explicit CSI feedback from the mobile stations in addition to the transmitted pilots. However, in case the channel reciprocity assumption does not hold, the mobile stations are required to estimate and feedback the downlink cross-channels, i.e. CSI, to the IA central unit.
Secondly, IA for the uplink is similar to IA for the downlink in terms of estimated quantities. A difference, at least from a practical point of view, is the required communication between the mobile stations needed to convey the channel estimates and the calculated precoders. For this reason, the IA for the downlink is probably more practical to determine with current system design considerations.
Few works have investigated how to efficiently share CSI on capacity-limited backhaul links targeting downlink closed-form IA with requirement of acquiring global CSI. However, there has been extensive research concentrated on limited feedback from receivers to the transmitters. In those scenarios where the receivers quantize and feedback the CSI to the transmitters, the problem is explored over frequency selective channels for single-antenna users, as in “Interference alignment with limited feedback” to J. Thukral and H. Bolcskei, published in Proc. IEEE Int. Symp. Information Theory (ISIT), Seoul, date June 2009, and for multiple-antenna users, as in “Interference alignment under limited feedback for MIMO interference channels”, to R. T. Krishnamachari and M. K. Varanasi, published in Proc. IEEE Int. Symp. Information Theory (ISIT), Austin, Tex., in June 2010. These papers provide “Degrees of Freedom”-achieving quantization schemes and study the required scaling of the number of feedback bits. For arbitrary channel coefficients in MIMO IC, as in “Limited feedback for interference alignment in the k-user MIMO interference channel”, to M. Rezaee and M. Guillaud, published in Proc. IEEE Inf. Theory. Workshop (ITW), Lausanne, provides the best currently known scaling of feedback bits to achieve IA. For broadcast channel, the scaling of the feedback bits was characterized in “MIMO broadcast channels with finite-rate feedback”, to N. Jindal, published in IEEE Trans. Inf. Theory, vol. 52, no. 11, pp. 5045-5060, in November 2006. Quantization of the precoding matrix using a Random Vector Quantization (RVQ) codebooks is investigated in “Capacity of a multiple-antenna fading channel with a quantized precoding matrix”, to W. Santipach and M. L. Honig, published in IEEE Trans. Inf. Theory, vol. 55, no. 3, pp. 1218-1234, March 2009. This paper provides insights on the asymptotic optimality of RVQ codebooks. From another point of view, as in “Cellular interference alignment with imperfect channel knowledge”, to Roland Tresch and Maxime Guillaud, published in Proc. IEEE International Conference on Communications (ICC), Dresden, Germany, date June 2009, an analysis of the effect of imperfect CSI on the mutual information of the interference alignment scheme is provided.
Existing interference alignment solutions for TDD typically calculate the IA precoders based on measured CSI in for example the uplink. As channel reciprocity is assumed, the measured CSI corresponds to the downlink as well. The so obtained CSI is quantized at each respective node before sending the quantized CSI to the IA central unit, e.g. a coordinating BS for downlink IA or a coordinating MS for uplink IA.
Some efficient code-book based CSI method exploit Grassmannian subspace packing. These methods avoid the typically less efficient direct quantization of the CSI. Instead, a transformed representation of the interfering channels at the receiver is quantized and represented by a code-book index. This is applicable when the receiver can convey the CSI over a feedback-link to the IA central unit. However, for interference alignment with TDD and no feedback-link for the CSI, this solution cannot be applied since the measured cross-channels are not the required ones, i.e., the set of outgoing cross-channels at the Tx side is different from the set of incoming cross-channels at the Rx side. A disadvantage is that the CSI feedback consumes resources of the feedback-link, which typically is a scarce radio interface between the BS and MS.